时间模上高阶动力学方程的有界解的振动性(英文)

On the Oscillatory Behavior of Bounded Solutions of Higher Order Dynamic Equation on Time Scales

摘要: 给出了时间模上的高阶动力学方程xΔ(n)(t)+f(t,x(t))=0的有界解振动或趋向于0的充分必要条件,即:当n是偶数时解是振动的;当n是奇数时解要么是振动的,要么是趋向于0.该文所用方法为研究时间模上高阶动力学方程的振动性提供了新的方法,且所得结果也统一和推广了连续和离散的动力学系统的理论.

Abstract: It is given sufficient and necessary conditions of the bounded solutions ofx~Δ(n)(t)+f(t,x(t))=0,which are oscillatory for n even and are oscillatory or tend monotonically to zero as t→∞ for n odd.We offer a new method on studying the oscillation of higher order dynamic equation on time scales.And the results generalize the theory of continuous and discrete dynamic equation.